Fingerprint Classification
Handbook of Fingerprint Recognition
Chapter 5 (5-1 and 5-2)
&
Fingerprint Classification by
Directional Image Partitioning
Raffaele Cappelli, Alessandra Lumini,
Dario Maio and Davide Maltoni. IEEE TRANSACTIONS ON PATTERN ANALYSIS AND
MACHINE INTELLIGENCE, vol. 21, no. 5, pp. 402-421, 1999.
Instructors: Dr. George Bebis and Dr. Ali Erol.
Presented by: Milind Zirpe.
CS 790Q (Fall 2005).
Overview
• Fingerprint Classification
– Introduction.
– Main classification techniques.
Introduction
• Need for fingerprint classification
– Database of fingerprints may be very large (e.g. several
million fingerprints).
– Leads to long response time and hence unsuitable in
real time applications.
– To reduce the number of comparisons.
Introduction
• What is fingerprint classification ?
Fingerprint classification refers to the problem of
classifying a fingerprint to a class in a consistent and
reliable way.
• An approach
A common strategy is to divide the fingerprint database
into a number of bins, based on some predefined
classes. A fingerprint to be identified is then required to
be compared only to the fingerprints in a single bin of
database based on its class.
Introduction
• Galton-Henry classification (Galton, 1892 and Henry, 1900).
Introduction
• A difficult pattern recognition problem
Introduction
• A difficult pattern recognition problem
Classification Techniques
Classification Techniques
1. Rule-based approaches
Classification according to the number and position of the
singularities (commonly used by human experts for manual
classification).
Classification Techniques
a. Kawagoe and Tojo (1984)
– Derive a coarse classification using type and position of singular
points.
– Finer classification is obtained by tracing the ridge line flow.
Classification Techniques
b. Karu and Jain (1996)
An iterative regularization (smoothening orientation image with a 3x3
box filter) is done until a valid number of singular points are detected.
This allows reducing noise and thus improves classification accuracy.
•
Criteria for differentiating between tented arches and loops
Connect the two singularities with a straight line and measure the avg.
difference between the local orientations along the line and the slope
of the line. A fingerprint is classified as a tented arch if:
Classification Techniques
• Problems with Rule-based approaches:
– Although simple, some problems arise in presence of noisy or
partial fingerprints, where singularity detection can be extremely
difficult. (Addressed to some extent by Karu and Jain (1996)
approach).
– May work well on rolled (nail to nail) fingerprint impressions
scanned from cards, but are not suitable for dab (live-scan)
fingerprint images, because delta points are often missing in
these types of images.
Classification Techniques
2. Syntactic approaches
– A syntactic method describes patterns by means of terminal symbols
and production rules.
– Terminal symbols are associated to small groups of directional elements
within the orientation image and represent a class.
– A grammar is defined for each class and a parsing process is
responsible for classifying each new pattern (Fu and Booth, 1986a, b).
Classification Techniques
a. Rao and Balck (1980)
– A ridge line is analyzed and represented by a set of connected lines.
– These lines are labeled according to the direction changes, thus
obtaining a set of strings that are processed through ad hoc
grammars or string-matching techniques to derive the final
classification.
Classification Techniques
• Problems with Syntactic approaches:
– Due to the great diversity of fingerprint patterns, syntactic
approaches require very complex grammars whose inference
requires complicated and unstable approaches.
Classification Techniques
3. Structural approaches
Based on the relational organization of low-level features into
higher-level structures. This relational organization is represented by
means of symbolic data structures (viz. trees and graphs), which
allow a hierarchical organization of the information (Bunke, 1993).
Classification Techniques
a. Maio and Maltoni (1996)
– The directional image is partitioned into several homogenous
regular-shaped regions, which are used to build a relational
graph summarizing the fingerprint macro-features.
– Directional image is computed, over a discrete grid 32x32, using
a robust technique proposed by Donahue and Rokhlin (1993).
– A dynamic clustering algorithm, Maio and Maltoni (1996), is
adopted to segment the directional image.
– A relational graph is built by creating a node for each region and
an arc for each pair of adjacent regions.
– An inexact graph matching technique, derived from Bunke and
Allermann (1983), is used to compute a “distance” vector
between the graph and each class prototype graph.
Classification Techniques
Class prototype graphs
Fig.3. Main steps. The intermediate results produced during the classification of a Left Loop fingerprint are shown.
Classification Techniques
• Advantages:
– The relational graphs are invariant with respect to displacement
and rotation of image.
– The technique neither requires any position alignment nor any
normalization.
– In principle, can be directly used for classification of partial
fingerprints (i.e., matching a graph with a sub graph).
• Problems with Structural approaches:
– It is not easy to robustly partition the orientation image into
homogenous regions, especially in poor quality fingerprints.
(Resolved to some extent by Cappelli et al. (1999) using
template-based matching).
Classification Techniques
4. Multiple classifier-based approaches
Different classifiers offer complementary information about the
patterns to be classified. This motivates combining of different
approaches for the fingerprint classification task.
Classification Techniques
a. Candela et al. (1995)
– Based on Neural Network and Rule-based approaches.
– The system is called as PCASYS (Pattern-level Classification
Automation SYStem).
– A probabilistic neural network is coupled with an auxiliary ridge
tracing module, specifically designed to detect whorl fingerprints.
Classification Techniques
Fig. A functional scheme of the PCASYS.
Classification Techniques
b. Jain, Prabhakar, and Hong (1999)
– Two stage classification strategy based on Statistical and Neural
Network approaches.
– Stage 1: A k-nearest neighbor classifier is used to find the two
most likely classes from a FingerCode feature vector (section 4.6).
– Stage 2: A specific neural network, trained to distinguish between
the two classes, is utilized to obtain the final decision. A total of 10
neural networks are trained to distinguish between each possible
pair of classes.
Classification Techniques
Fingerprint Classification by
Directional Image Partitioning
Raffaele Cappelli, Alessandra Lumini,
Dario Maio and Davide Maltoni.
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE
INTELLIGENCE, vol. 21, no. 5, pp. 402-421, 1999.
Overview
• Fingerprint Classification by Directional
Image Partitioning
–
–
–
–
–
Introduction.
The new approach.
Fingerprint retrieval.
Experimental results.
Conclusion.
Introduction
• The relational graph approach has some problems in
obtaining analogous segmentation from similar directional
images.
• Influenced too much by local ridge-line orientation
changes, start point of clustering routines.
• The new approach uses dynamic masks for directional
image partitioning.
• It is translation and rotation invariant and does not require
the singularities to be detected.
Introduction
Fig. 4. The segmentation of two Left Loop fingerprints.
The New Approach
•
•
•
•
•
•
Overview of the new approach.
Directional image computation and enhancement.
Dynamic mask definition.
Directional image partitioning with Dynamic masks.
Generation of a set of Prototype masks.
Classification.
Overview of the new approach
• The basic idea of the new approach is to perform a “guided”
segmentation of the directional image with the aim of drastically
reducing the degrees of freedom during the partitioning process,
conferring stability to the solutions.
• A set of dynamic masks, directly derived from the most common
fingerprint classes, are used to guide the partitioning.
• The inexact graph matching step is simplified and embedded in the
segmentation step.
Overview of the new approach
Fig. 6. Classification of a Left Loop fingerprint by means of the dynamic masks approach.
Directional image computation and
enhancement
• Directional image computation:
– The finger area is separated from the background and its quality
is improved by a filtering in the frequency domain.
– The R.M. Stock and C.W. Swonger (1969) method is applied to
calculate directional elements. Each element is represented by a
vector v.
• Directional image enhancement:
– Regularization:
Regularization of directional elements by local averaging on 3x3
windows W.
Directional image computation and
enhancement
• Directional image enhancement (contd.):
– Attenuation:
Attenuation of the border elements by applying a Gaussian-like function
which progressively reduces the element magnitude moving from the
center towards the borders.
where distc(v) returns the distance in blocks of v origin from the
directional image center and s determines the scale of the Gaussian
function.
Directional image computation and
enhancement
• Directional image enhancement (contd.):
– Strengthening:
We use a strengthening function (str) which increases the significance of
each element according to the irregularity degree of its 3x3 neighborhood,
without requiring the singularities to be explicitly detected.
returns 0 if all the vectors are parallel to each other and its value
approaches 1 when discordance increases.
The resulting directional image is made up of vectors ve such that:
where
is a weighting factor.
Directional image computation and
enhancement
Fig. 7. Enhancement of a directional image: the map in the arrow-box shows the
most irregular regions as revealed by the str function. The parameters
are: s = 9.6 and l = 112.
Dynamic mask definition
• Dynamic masks have been introduced in order to decrease the
degrees of freedom during the partitioning process.
• Each mask is characterized by a set of vertices defining the borders
of the regions which determine the segmentation.
• Some vertices can be locally moved to best fit the fingerprint image
singularities, which can occupy different positions within fingerprints
of the same class.
Fig. 8. The singularity positions in three different Left Loop fingerprints.
Dynamic mask definition
• Formally, a dynamic mask is defined as a 6-tuple:
M=
,
where:
– V=
is a set of vertices p.
– P=
is a set of polygonal regions whose vertices are in V.
–
is a relation, encoding the dependency of the dependent
vertices from the mobile ones. Each dependent vertex is anchored to
exactly one mobile vertex.
–
encodes a relation between some region pairs. For
each pair Pi, Pj, whose orientation difference
is significant, the
triplet
.
–
is a function which associates to each mobile
vertex a mobility window which limits the vertex movements during the
mask adaptation.
–
is a function which indicates, for each pair in
the dependent vertex movement on the basis of the corresponding
mobile vertex movement.
Dynamic mask definition
Fig. 9. An example of dynamic mask definition. Fixed vertices are denoted by empty circles, the
mobile ones by black circles, and the dependent ones by gray circles. The dashed boxes denote
the mobility windows associated to the mobile vertices. An arrow from a mobile vertex pi to a
dependent vertex pj indicates the dependence of pj on pi.
Directional image partitioning with
Dynamic masks
• Let MT,Q be the steady mask obtained by the dynamic mask M as a
result of the following transformations:
– a global rotation-displacement T =
where
and denote
the global mask displacement and denotes the global mask rotation.
– a set of mobile vertex displacements Q = { (dx1, dy1), (dx2, dy2), ... }; (dxi,
dyi) denotes the displacement of the vertex pi with respect to its initial
position.
• The application of a steady mask MT,Q to a directional image D
consists in superimposing MT,Q on D and deriving a segmentation R
= {R1, R2, ..., Rn} where each region Ri is made up of the directional
elements internal to the polygon Pi.
Directional image partitioning with
Dynamic masks
• The cost Csm(MT,Q, D) of the application of MT,Q to D is given by the sum
of two terms:
where:
First term: Var(Ri) is proportional to the variance of the directional elements in
Ri and C0 is a parameter which introduces a penalty proportional to the number
of regions in M in order to balance the possibility of obtaining lower costs by
segmenting the directional image into several small regions.
Second term:
returns the difference between the avg. orientations of
regions Ri and Ri;
returns the difference between qi, qj; μ is the
weight of the orientation difference contribution, and
returns the number
of triplets in
.
Directional image partitioning with
Dynamic masks
• The application cost of a dynamic mask M to a directional image D is
computed by determining the minimum cost
over all the
possible steady masks MT,Q :
Directional image partitioning with
Dynamic masks
Fig. 10. Adaptation of the mask defined in Fig. 9 to three different images of the
same Left Loop fingerprint.
Generation of a set of Prototype masks
Fig. 11. Prototype mask creation. The mask area is larger than the directional image to allow
the border elements to be considered during the mask displacement.
Generation of a set of Prototype masks
Fig. 11 (contd.). Prototype mask creation. The mask area is larger than the directional image
to allow the border elements to be considered during the mask displacement.
Generation of a set of Prototype masks
Fig. 12. The five prototype masks derived from the classes Arch, Left Loop, Right Loop,
Tented Arch, and Whorl. The vertex positions, the mobility windows, and the dependencies on
mobile vertices are graphically shown.
Generation of a set of Prototype masks
Fig. 12 (contd.). Example of application of each mask to a fingerprint belonging to the
corresponding class.
Classification
• Let Mi, i = 1..s be the prototype masks and D the directional image to be
classified; the feature vector wD resulting from the mask application is:
where low component values denote high similarity with the
corresponding prototype mask.
• wD can be normalized as:
• The normalization enables:
– working within the fixed range [0, 1]; this makes fingerprint indexing through
spatial data structures easier.
– dealing with differently contrasted images: The image contrast is related to
the magnitude of the directional elements; hence, it can determine an
increase or a reduction of all the costs.
Classification
Fig. 13. The figure shows the segmentation obtained by applying the prototype masks defined
in Fig. 12 to some sample fingerprints (only one example is provided for each class); the
corresponding normalized feature vectors are shown on the right in the form of histograms.
Classification
Fig. 13. (contd.)
Fingerprint retrieval
• Exclusive classification:
A neural network or a statistical classifier can be used to properly
classify vectors
.
• Continuous classification:
itself can be used as an access key for similarity searches. (Each
fingerprint is characterized with a numerical vector).
• In order to evaluate the efficiency of continuous vs. exclusive
classification for latent fingerprint retrieval, two different methodologies
were proposed (A. Lumini, D. Maio, D. Maltoni, 1997), named A and B.
• Four different strategies: AE, AC, BE, BC.
Fingerprint retrieval
• Methodology A:
Methodology A assumes an error-free classification, so the search is
restricted to the database fingerprints resembling analogous
classification characteristics.
AE:
The strategy AE can be implemented by searching the whole corresponding
class of the latent fingerprint.
– The average portion of database considered:
Where, Pd(i) represents the database fraction involved in the retrieval of a fingerprint
of class i and Pc(i) is the weighting factor representing the probability to classify a
latent fingerprint as i.
– The average retrieval error:
Where, Pd|c(j|i) represents the conditional probability that a database fingerprint,
corresponding to a latent fingerprint classified as i, has been classified j in the
database.
Fingerprint retrieval
• Methodology A:
AC:
The strategy AC can be implemented by searching among those fingerprints
which are less far from the feature vector w of the latent fingerprint than a
fixed tolerance ρ.
Given a fixed ρ,
– The average portion of database considered Cρ(AC) is determined by the
average number of fingerprints inside the hyper-sphere with radius ρ,
centered in the latent fingerprint.
– The average retrieval error Eρ(AC) is determined by the average number of
missed retrievals inside the search area.
Fingerprint retrieval
• Methodology B:
– Methodology B allows for misclassification to be taken into account;
to this aim, the search is carried out incrementally over the whole
database, avoiding any possible retrieval error.
– This methodology requires the search to be terminated when a
human expert finds a real correspondence between the latent
fingerprint and a database fingerprint that has already been
considered.
BE:
The strategy BE can be implemented by starting the search from the latent
fingerprint class, and incrementally extending it to the other classes.
BC:
The strategy BC can be carried out by processing fingerprints according to
their distance from the latent fingerprint feature vector w.
Experimental results
• Databases used:
– NIST Special Database 4 (Db4) contains 2,000 fingerprint pairs, uniformly
distributed in the five classes, in order to resemble a real distribution.
– NIST Special Database 14 (Db14) contains 27,000 fingerprint pairs
randomly taken, thus approximating the real fingerprint distribution; only the
last 2,700 fingerprint pairs have been employed in the simulation.
– The first 2,000 fingerprints of Db14 have been used as “training set” to
derive the set of prototype masks and to optimize the parameters.
– MASK: the dynamic mask method introduced in this paper.
– LUMINI: the continuous classification approach described in A. Lumini, D.
Maio, D. Maltoni (1997).
– PCASYS: the exclusive approach by NIST (G.T. Candela, et al., 1995).
Experimental results
Fig. 14. MASK results over Db4 (a) and Db14 (b); the average portion of database considered
Cρ(AC) and the average retrieval error Eρ(AC) are plotted as a function of ρ.
Experimental results
Fig. 15. Trade-off Cρ(AC)/Eρ(AC) varying ρ for the two continuous approaches MASK and
LUMINI. The point
denotes C(AE)/E(AE) for the exclusive classification approach PCASYS.
Experimental results
TABLE 1: STRATEGY AC: COMPARISON BETWEEN LUMINI AND MASK.
Experimental results
TABLE 2: COMPARISON AMONG PCASYS, LUMINI, AND MASK FIXING THE AVERAGE PORTION
OF DATABASE READ.
TABLE 3: COMPARISON BETWEEN THE AVERAGE PERCENTAGES OF DATABASE SEARCHED
(METHODOLOGY B).
Experimental results
TABLE 5: CLASSIFICATION OF SOME FINGERPRINT IMAGES SUBMITTED TO ARTIFICIAL
PERTURBATIONS. (Robustness).
Experimental results
TABLE 8: AVERAGE TIME SPENT FOR THE MAIN PROCESSING STEPS.
Conclusion
• Dynamic masks have been defined as a powerful instrument for
a robust segmentation. (Noisy and partial fingerprint images).
• The experimental results prove the accuracy and robustness of
the new method.
• The comparison with other techniques demonstrates its
superiority for the continuous classification task, especially if
fingerprints are classified only for improving the retrieval
efficiency.
• Continuous classification does not enable to accomplish some
tasks to be carried out, such as fingerprint labeling according to a
given classification scheme.
Thank you.